Tag Archives: Rrt

Path planning by merging random sampling (RRT) with informed heuristics (A*)

Jonathan D Gammell, Timothy D Barfoot, Siddhartha S Srinivasa, Batch Informed Trees (BIT*): Informed asymptotically optimal anytime search, The International Journal of Robotics Research. 2020;39(5):543-567, DOI: 10.1177/0278364919890396.

Path planning in robotics often requires finding high-quality solutions to continuously valued and/or high-dimensional problems. These problems are challenging and most planning algorithms instead solve simplified approximations. Popular approximations include graphs and random samples, as used by informed graph-based searches and anytime sampling-based planners, respectively.

Informed graph-based searches, such as A*, traditionally use heuristics to search a priori graphs in order of potential solution quality. This makes their search efficient, but leaves their performance dependent on the chosen approximation. If the resolution of the chosen approximation is too low, then they may not find a (suitable) solution, but if it is too high, then they may take a prohibitively long time to do so.

Anytime sampling-based planners, such as RRT*, traditionally use random sampling to approximate the problem domain incrementally. This allows them to increase resolution until a suitable solution is found, but makes their search dependent on the order of approximation. Arbitrary sequences of random samples approximate the problem domain in every direction simultaneously, but may be prohibitively inefficient at containing a solution.

This article unifies and extends these two approaches to develop Batch Informed Trees (BIT*), an informed, anytime sampling-based planner. BIT* solves continuous path planning problems efficiently by using sampling and heuristics to alternately approximate and search the problem domain. Its search is ordered by potential solution quality, as in A*, and its approximation improves indefinitely with additional computational time, as in RRT*. It is shown analytically to be almost-surely asymptotically optimal and experimentally to outperform existing sampling-based planners, especially on high-dimensional planning problems.

Hybridizing RRT with deliberative path planning to improve performance

Dong, Y., Camci, E. & Kayacan, Faster RRT-based Nonholonomic Path Planning in 2D Building Environments Using Skeleton-constrained Path Biasing, J Intell Robot Syst (2018) 89: 387, DOI: 10.1007/s10846-017-0567-9.

This paper presents a faster RRT-based path planning approach for regular 2-dimensional (2D) building environments. To minimize the planning time, we adopt the idea of biasing the RRT tree-growth in more focused ways. We propose to calculate the skeleton of the 2D environment first, then connect a geometrical path on the skeleton, and grow the RRT tree via the seeds generated locally along this path. We conduct batched simulations to find the universal parameters in manipulating the seeds generation. We show that the proposed skeleton-biased locally-seeded RRT (skilled-RRT) is faster than the other baseline planners (RRT, RRT*, A*-RRT, Theta*-RRT, and MARRT) through experimental tests using different vehicles in different 2D building environments. Given mild assumptions of the 2D environments, we prove that the proposed approach is probabilistically complete. We also present an application of the skilled-RRT for unmanned ground vehicle. Compared to the other baseline algorithms (Theta*-RRT and MARRT), we show the applicability and fast planning of the skilled-RRT in real environment.

On the drawbacks of RRT and how including deterministic sampling can help

Lucas Janson, Brian Ichter, and Marco Pavone, Deterministic sampling-based motion planning: Optimality, complexity, and performance , The International Journal of Robotics Research Vol 37, Issue 1, pp. 46 – 61, DOI: 10.1177/0278364917714338.

Probabilistic sampling-based algorithms, such as the probabilistic roadmap (PRM) and the rapidly exploring random tree (RRT) algorithms, represent one of the most successful approaches to robotic motion planning, due to their strong theoretical properties (in terms of probabilistic completeness or even asymptotic optimality) and remarkable practical performance. Such algorithms are probabilistic in that they compute a path by connecting independently and identically distributed (i.i.d.) random points in the configuration space. Their randomization aspect, however, makes several tasks challenging, including certification for safety-critical applications and use of offline computation to improve real-time execution. Hence, an important open question is whether similar (or better) theoretical guarantees and practical performance could be obtained by considering deterministic, as opposed to random, sampling sequences. The objective of this paper is to provide a rigorous answer to this question. Specifically, we first show that PRM, for a certain selection of tuning parameters and deterministic low-dispersion sampling sequences, is deterministically asymptotically optimal, in other words, it returns a path whose cost converges deterministically to the optimal one as the number of points goes to infinity. Second, we characterize the convergence rate, and we find that the factor of sub-optimality can be very explicitly upper-bounded in terms of theℓ2 -dispersion of the sampling sequence and the connection radius of PRM. Third, we show that an asymptotically optimal version of PRM exists with computational and space complexity arbitrarily close to O(n) (the theoretical lower bound), where n is the number of points in the sequence. This is in contrast to the O(nlogn) complexity results for existing asymptotically optimal probabilistic planners. Fourth, we discuss extending our theoretical results and insights to other batch-processing algorithms such as FMT*, to non-uniform sampling strategies, to k-nearest-neighbor implementations, and to differentially constrained problems. Importantly, our main theoretical tool is the ℓ2-dispersion, an interesting consequence of which is that all our theoretical results also hold for low-ℓ2-dispersion random sampling (which i.i.d. sampling does not satisfy). In other words, achieving deterministic guarantees is really a matter of i.i.d. sampling versus non-i.i.d. low-dispersion sampling (with deterministic sampling as a prominent case), as opposed to random versus deterministic. Finally, through numerical experiments, we show that planning with deterministic (or random) low-dispersion sampling generally provides superior performance in terms of path cost and success rate.

Study of how a complex motion planning problem solved through RRT can benefit from parallelization

Brian W. Satzinger, Chelsea Lau, Marten Byl, Katie Byl, Tractable locomotion planning for RoboSimian, The International Journal of Robotics Research November 2015 vol. 34 no. 13 1541-1558, DOI: 10.1177/0278364915584947.

This paper investigates practical solutions for low-bandwidth, teleoperated mobility for RoboSimian in complex environments. Locomotion planning for this robot is challenging due to kinematic redundancy. We present an end-to-end planning method that exploits a reduced-dimension rapidly-exploring random tree search, constraining a subset of limbs to an inverse kinematics table. Then, we evaluate the performance of this approach through simulations in randomized environments and in the style of the Defense Advanced Research Projects Agency Robotics Challenges terrain both in simulation and with hardware.
We also illustrate the importance of allowing for significant body motion during swing leg motions on extreme terrain and quantify the trade-offs between computation time and execution time, subject to velocity and acceleration limits of the joints. These results lead us to hypothesize that appropriate statistical “investment” of parallel computing resources between competing formulations or flavors of random planning algorithms can improve motion planning performance significantly. Motivated by the need to improve the speed of limbed mobility for the Defense Advanced Research Projects Agency Robotics Challenge, we introduce one formulation of this resource allocation problem as a toy example and discuss advantages and implications of such trajectory planning for tractable locomotion on complex terrain.